An example of previously know N-time cyclic filters is shown in a block diagram in FIG. 2. In the figure, numbers 1 through 4 indicate unit delay elements providing a unit delay D each, which are connected in series; 5 is an input adder; 6 is an output adder; 7 through 14 are multipliers for weighing the unit delay elements 1 through 4 by coefficients a.sub.1, a.sub.2, a.sub.N-1, a.sub.N, b.sub.1, b.sub.2, b.sub.N-1 and b.sub.N, respectively, the multiplier 7 being connected between an output of the unit delay element 1 and the input adder 5, the multiplier 11 being connected between the output of the unit delay element 1 and the output adder 6, the multiplier 8 being connected between an output of the unit delay element 2 and the input adder 5, the multipler 12 being connected between the output of the unit delay element 2 and the output adder 6, the multipler 9 being connected an output of the unit delay element 3 and the input adder 5, the multiplier 13 being connected between the output of the unit delay element 3 and the output adder 6, the multiplier 10 being connected between an output of the unit delay element 4 and the input adder 5, and the multiplier 14 being connected to between the output of the unit delay element 4 and the output adder 6.
A system function H(z) of the N-time cyclic filer shown in FIG. 2 is given as ##EQU1## where x is an input data, y is an output data and z is a unit delay operator. There are shown delay data D.sub.0, D.sub.1, D.sub.2 to D.sub.N-1 and D.sub.N across the respective unit delay elements 1, 2, 3 and 4. To obtain the output data y, it is required to perform 2N times of multiplication, 2N times of addition and 2N times of update of the delay data D.sub.0, D.sub.1, D.sub.2 to D.sub.N-1 and D.sub.N. This can be expressed as ##EQU2##
As described above, the previous N-time cyclic filers can process known digital signals; but, they cannot process signals for which coefficients have to be rewritten in a real time fashion because they have no means for writing the coefficients in the real time fashion.
In addition, it has previously been proposed to provide a method of musical tone generation that a semiconductor memory has a wave or a plurality of waves stored for every semitone in a whole tone range over which the electronic musical instrument covers and the wave or waves are read with a specific sampling interval. Also, it has previously been proposed to provide another method of musical tone generation that a semiconductor memory stores a wave or a plurality of waves of a specific tone or a plurality of specific tones in a whole tone range over which the electronic musical instrument covers and the wave or waves are read with a variable sampling time.
The electronic musical instruments constructed in the above mentioned methods read the wave or waves at a particular sampling rate, or have waveform data corresponding to the respective pitch detectors such as keys thereof to change the pitch at a variable sampling rate. Such electronic musical instruments involve a problem that enormous memory capacity is needed as the amount of addresses becomes large when the pitch is lowered.
Further, it has previously been proposed to provide a method that a memory has a wave or waves of a very long address or addresses stored with a bandwidth limited, sampled values are extracted appropriately, and the wave or waves are output at a specific sampling rate. This method, also, needs enormous addresses to reproduce correct tones. The method, further, involves a difficulty in generating tones in a wider frequency range. The difficulty leads to a problem of folded error due to generation of a higher frequency tone when the tone needs to contain particularly high harmonics.
Furthermore, an electronic musical instrument that the wave or waves are read from at the variable sampling rate, involves a problem that a single D/A converter cannot function in a time-division multiprocess way; but, a plurality of D/A converters are needed to generate a multi-tone at one time.
More particularly, two of the N-time cyclic filters are of a type more specifically set forth in Japanese Laying-Open Patent Gazette No. 60-22192 issued Feb. 4, 1985 to Tahiro Murase. The electronic musical instrument disclosed in this gazette comprises a data memory for storing synthesized tone data, a data reader for reading the synthesized tone data from the data memory, and a waveform generator for generating a musical tone by using the synthesized tone data read by the data reader.
Furthermore particularly, two of the N-time cyclic filters are of a type more specifically set forth in Japanese Laying-Open Patent Gazette No. 59-136790 issued Aug. 6, 1984 to Tahiro Murase et al. The musical tone generation instrument disclosed in the gazette comprises a waveform memory for storing at least two of a plurality of musical tone waveforms from start of a tone generation to end, a note clock generator for determining a musical scale, a waveform reader for reading two waveform sampled data from the waveform memory depending on a signal output of the note clock generator, a waveform calculator for forming the musical waveform by using the two waveform sampled data read by the waveform reader, and a converter for converting to analog the digital signal output of the waveform calculator.